Flow plasticity theory: Difference between revisions

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=== Kinematics of multiplicative plasticity ===

The concept of multiplicative decomposition of the deformation gradient into elastic and plastic parts was first proposed independently by B. A. Bilby,<ref>{{Citation|last1=Bilby|first1=B. A.|last2=Bullough|first2=R.|last3=Smith|first3= E.|year=1955|title= Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry|journal= [[Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences]]|volume= 231|pages= 263–273.|issue=1185|bibcode=1955RSPSA.231..263B|doi=10.1098/rspa.1955.0171}}</ref> E. Kroner,<ref>{{Citation|last=Kroner|first=E.|title=Kontinuumstheorie der versetzungen und eigenspannungen|journal=Erg. Angew. Math.|volume= 5 |year=1958|pages=1–179.}}</ref> in the context of [[crystal plasticity]] and extended to continuum plasticity by Erasmus Lee.<ref>{{Citation|last=Lee|first= E. H. |year=1969|title=Elastic-Plastic Deformation at Finite Strains|journal= Journal of Applied Mechanics|volume= 36|pages= 1|url=ftp://melmac.sd.ruhr-uni-bochum.de/kintzel/JoaM_27_04_2008/Lee_69.pdf|doi=10.1115/1.3564580|bibcode = 1969JAM....36....1L }}</ref> The decomposition assumes that the total deformation gradient ('''''F''''') can be decomposed as:

:<math>

\boldsymbol{F} = \boldsymbol{F}^e\cdot\boldsymbol{F}^p